Multi-layer dissolution exponential-family models for weighted signed networks

TL;DR

This paper introduces a novel multi-layer exponential random graph model for weighted signed networks, enabling joint analysis of relationship sign and strength with Bayesian inference, demonstrated on US Senate data.

Contribution

It presents a new statistical framework that jointly models signed and weighted network data, incorporating Bayesian hierarchical methods for improved inference.

Findings

Revealed complex signed and weighted interaction patterns in Senate data

Demonstrated the model's ability to assess structural balance effects

Showed improved inference over traditional methods

Abstract

Understanding the structure of weighted signed networks is essential for analysing social systems in which relationships vary both in sign and strength. Despite significant advances in statistical network analysis, there is still a lack of statistical models that can jointly and rigorously account for both the sign and strength of relationships in networks. We introduce a multi-layer dissolution exponential random graph modelling framework that jointly captures the signed and weighted processes, conditional on the observed interaction structure. The framework enables rigorous assessment of structural balance effects while fully accounting for edge weights. To enhance inference, we adopt a fully-probabilistic Bayesian hierarchical approach that partially pools information across layers, with parameters estimated via an adaptive approximate exchange algorithm. We demonstrate the flexibility and explanatory power of the proposed methodology by applying it to bill sponsorship data from the 108th US Senate, revealing complex patterns of signed and weighted interactions and structural balance effects that traditional approaches are unable to capture.